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1.

This study analyzes six seventh grade Israeli mathematics textbooks, examining (1) the extent to which students are required to justify and explain their mathematical work, and (2) whether students are asked to justify a mathematical claim that is stated by the textbook or a mathematical claim that they themselves generated when solving a problem. Two different units of analysis were used to analyze two central topics in the seventh grade curriculum as follows: (1) equation solving in algebra and (2) triangle properties in geometry. The findings indicate that all six textbooks had considerably larger percentages of geometric tasks than algebraic tasks, which required students to justify or explain their mathematical work. Moreover, considerable differences were found among the six textbooks regarding the percentages of tasks that required students to justify and explain in both topics, but more so with the algebraic topic. Analysis of whether the textbook tasks required students to justify a mathematical claim that is stated by the textbook or a mathematical claim that the students themselves generated also revealed substantial differences among the textbooks. These findings are discussed, as well as the research methods used, in light of relevant literature.

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2.
The aim of this study is to analyse how mathematical problem solving is represented in mathematical textbooks for Swedish upper secondary school. The analysis comprises dominating Swedish textbook series, and relates to uncovering (a) the quantity of tasks that are actually mathematical problems, (b) their location in the chapter, (c) their difficulty level, and (d) their context. Based on an analysis of 5,722 tasks from the area of calculus, it is concluded that the textbooks themselves contain very few tasks that can be defined as mathematical problems, and that those that are mathematical problems are found at the end of a chapter at the most difficult level, and are presented in a pure mathematical context. Implications are discussed.  相似文献   

3.
Coordination of multiple representations (CMR) is widely recognized as a critical skill in mathematics and is frequently demanded in reform calculus textbooks. However, little is known about the prevalence of coordination tasks in such textbooks. We coded 707 instances of CMR in a widely used reform calculus textbook and analyzed the distributions of coordination tasks by chapter and for the type of task demanded (perception vs. construction). Results suggest that different coordination tasks are used earlier and later in learning and for different topics, as well as for specific pedagogical and scaffolding purposes. For example, the algebra-to-text coordination task was more prevalent in the first chapter, suggesting that students are being eased into calculus content. By contrast, requests to construct graphs from algebraic expressions were emphasized in later chapters, suggesting that students are being pushed to think more conceptually about functions. Our nuanced look at coordination tasks in a reform textbook has implications for research in teaching and learning calculus.  相似文献   

4.

This study compares students’ opportunities to engage in transformational (rule-based) algebraic activity between 2 classes taught by the same teacher and across 2 topics in beginning algebra: forming and investigating algebraic expressions and equivalence of algebraic expressions. It comprises 2 case studies; each involves a teacher teaching in two 7th grade classes. All 4 classes used the same textbook. Analysis of classroom videotapes (15–19 lessons in each class) revealed that the opportunities to engage in transformational algebraic activity related to forming and investigating algebraic expressions were similar in each teacher’s 2 classes. By contrast, substantial differences were found between 1 teacher’s classes with regard to the opportunities to engage in transformational algebraic activity related to equivalence of algebraic expressions. The discussion highlights the contribution of the interplay among the mathematical topic, the teacher, and the class to shaping students’ learning opportunities. Specifically, the mathematical topic appeared to play a prominent role in certain situations, with the topic involving deductive reasoning generating high variation in classes of 1 teacher but not in the other’s.

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5.
This study examines how students’ opportunities to engage in argumentative activity are shaped by the teacher, the class, and the mathematical topic. It compares the argumentative activity between two classes taught by the same teacher using the same textbook and across two beginning algebra topics—investigating algebraic expressions and equivalence of algebraic expressions. The study comprises two case studies in which each teacher taught two 7th grade classes. Analysis of classroom videotapes revealed that the opportunities to engage in argumentative activity with the topic investigating algebraic expressions were similar in each teacher's two classes. By contrast, substantial differences were found between one teacher's classes with regard to the opportunities to engage in argumentative activity with the topic equivalence of algebraic expressions. The discussion highlights how the interplay between the characteristics of the mathematical topic, the characteristics of the class, and the characteristics of the teacher contributed to the shaping of students’ opportunities to engage in argumentative activity.  相似文献   

6.
This study compares students’ opportunities to engage in transformational (rule-based) algebraic activity between 2 classes taught by the same teacher and across 2 topics in beginning algebra: forming and investigating algebraic expressions and equivalence of algebraic expressions. It comprises 2 case studies; each involves a teacher teaching in two 7th grade classes. All 4 classes used the same textbook. Analysis of classroom videotapes (15–19 lessons in each class) revealed that the opportunities to engage in transformational algebraic activity related to forming and investigating algebraic expressions were similar in each teacher’s 2 classes. By contrast, substantial differences were found between 1 teacher’s classes with regard to the opportunities to engage in transformational algebraic activity related to equivalence of algebraic expressions. The discussion highlights the contribution of the interplay among the mathematical topic, the teacher, and the class to shaping students’ learning opportunities. Specifically, the mathematical topic appeared to play a prominent role in certain situations, with the topic involving deductive reasoning generating high variation in classes of 1 teacher but not in the other’s.  相似文献   

7.
A qualitative case study research was conducted to investigate the process of evaluation and implementation of a Standard-based textbook by two seventh grade middle school mathematics teachers over a period of two years. The data suggested that teachers' mathematical knowledge was the greatest influence on how they evaluated and implemented the textbook. This mathematical knowledge manifested itself in how the teachers planned their instruction, interacted with students, and used the textbook in their classes.This revised version was published online in September 2005 with corrections to the Cover Date.  相似文献   

8.
This paper reports on 2 studies that examine how mathematical problem posing is integrated in Chinese and US elementary mathematics textbooks. Study 1 involved a historical analysis of the problem-posing (PP) tasks in 3 editions of the most widely used elementary mathematics textbook series published by People’s Education Press in China over 3 decades. Study 2 compared the PP tasks in Chinese and US elementary mathematics textbooks. This allows for the examination of PP tasks from an international comparative perspective, which provides one point of view about the kinds of learning opportunities that are available to students in China and the USA. We found evidence that the inclusion of PP tasks in the Chinese textbook series reflected, to some degree, changes in the curricular frameworks in China. However, the distribution of PP tasks across grade levels and content areas, as well as the variety of types of PP tasks included, suggest a need for greater intentionality in the design and placement of PP tasks in both the Chinese and US textbook series. Findings from the 2 studies reported in this paper not only contribute to our understanding about the inclusion of PP tasks in curriculum both historically and internationally, but also suggest a great need to systematically integrate PP activities into curriculum and instruction. The fact that both Chinese and US curriculum standards have heavily emphasized PP in school mathematics, despite there being only a small proportion of PP activities in both Chinese and US elementary mathematics curricula, suggests the existence of challenges that are delaying the implementation of reform ideas such as problem posing in school mathematics.  相似文献   

9.
This study explores how textbooks function in education. It asked whether opportunities provided in math textbooks to engage in tasks demanding different levels of understanding correlate with students’ achievements on tasks demanding equivalent levels of understanding on a standardized exam. The textbooks evaluated were two 8th grade mathematics textbooks used by students in the Arab community in Israel, showing that Textbook A makes more cognitive demands than Textbook B. The study correlated textbooks’ cognitive demand with the scores of all 8th grade students in the Arab community who completed the national math test in 2015 and studied in schools using either Textbook A or B (N = 4040), while attending to mediating variables. The findings show that if a textbook provides the opportunity to engage in tasks demanding higher levels of understanding, students using this book will have higher scores. The study shows that gender and SES play an important role in how opportunities provided in textbooks interact with students’ scores. Many factors influence variations in mathematics achievements within and between nations. The findings illuminate textbooks’ ability to provide opportunities to learn mathematics. As a result, they raise new questions about how teachers use textbooks and about the role of textbooks in promoting access and equity in mathematics education. Although the work explored specific textbooks, its findings shed light on how learning opportunities relate to achievements more generally.  相似文献   

10.
This paper focuses on one aspect of mathematical competence, namely mathematical reasoning, and how this competency influences students’ knowing of physics. This influence was studied by analysing the mathematical reasoning requirements upper secondary students meet when solving tasks in national physics tests. National tests are constructed to mirror the goals stated in the curricula, and these goals are similar across national borders. The framework used for characterising the mathematical reasoning required to solve the tasks in the national physics tests distinguishes between imitative and creative mathematical reasoning. The analysis process consisted of structured comparisons between representative student solutions and the students’ educational history. Of the 209 analysed tasks, 3/4 required mathematical reasoning in order to be solved. Creative mathematical reasoning, which, in particular, involves reasoning based on intrinsic properties, was required for 1/3 of the tasks. The results in this paper give strong evidence that creative mathematical reasoning is required to achieve higher grades on the tests. It is also confirmed that mathematical reasoning is an important and integral part of the physics curricula; and, it is suggested that the ability to use creative mathematical reasoning is necessary to fully master the curricula.  相似文献   

11.
This study describes a comparison of how worked examples in selected textbooks from England and Shanghai presented possible learning trajectories towards understanding linear function. Six selected English textbooks and one Shanghai compulsory textbook were analysed with regards to the understanding required for pure mathematics knowledge in linear function. Understanding was defined as being at five levels: Dependent Relationship, Connecting Representations, Local Properties Noticing, Object Analysis and Inventising. These levels were developed by examining the most prominent theories from the existing literature on understanding function. Findings suggested that the English textbooks constrained the structural aspect of understanding linear function due to a point-to-point view of function, while the Shanghai textbook which focussed on a variable view of function overemphasised the algebraic approach. The discussion explored the drawbacks to each approach and what teachers or textbook writers could do to balance these two approaches in order to facilitate students’ understanding towards a structural view of linear function.  相似文献   

12.
Listening is important for college students,especially for students who are majoring in English and it is also the most difficult part of English study.So it is quite important to choose a good listening textbook,however,traditional listening textbooks have so many disadvantages that it's hard for students to form a good habit for listening.Firstly,some disadvantages of traditional listening textbooks will be stated.And some suggestions will be given for a good listening textbook.Finally,the writer will give some advice to teachers who are teaching listening.  相似文献   

13.
Through the lenses of statistical investigations and cognitive demands, we examined bivariate data tasks offered in US high school mathematics textbook series—a popular representative of three curriculum types: traditional, integrated, and hybrid. We developed a framework grounded in literature of association topics for the inclusion and exclusion of tasks. Using the Guidelines for Assessment and Instruction of Statistics Education (GAISE) framework, textbook tasks were coded for four investigation components (formulate questions, collect data, analyze data, and interpret results) and levels of statistical sophistication, as well as levels of cognitive demand as suggested by the Mathematical Complexity framework. Across the three series 582 statistical association tasks, all components of statistical investigation were evident with different levels of treatment: (a) all questions for statistical investigations were provided by textbook authors; (b) tasks rarely afforded student opportunities to collect data; and (c) nearly all of the tasks required students to analyze data and most required them to interpret results. Tasks in the integrated series were more numerous (n = 246) and required higher levels of mathematical complexity and statistical sophistication than tasks in the traditional and hybrid series. The vast majority of tasks were coded at the GAISE Level B for analyze data and interpret results and moderate level for mathematical complexity. Further analyses show the concordance between the developmental levels for statistical sophistication and mathematical complexity. Suggestions for curriculum development, content analysis, and future research are provided.  相似文献   

14.
May Hamdan 《PRIMUS》2017,27(10):916-925
This paper reflects on a teaching experiment and presents details of a pedagogical technique where students periodically write down their clearest interpretation of the conditions imposed on various discrete mathematical subjects they are learning in class. Through iterations, students generate a more complete understanding of the material, one that they themselves can justify. This experiment was conducted in the Discrete Mathematical Structures course; as it contains several subtopics, each of which uses a discrete set of elements with specific conditions. The textbook does not mention how those conditions are effectively put to use, and often uses the natural numbers as the default domain. Students are required to identify in their journals the exact properties that the elements need to have, justify how they are being put to use, and in ambitious cases attempt to sharpen them if possible. This activity can be adapted to different contexts and is not specific to the topic of Discrete Mathematical Structures.  相似文献   

15.
This study examined the effects of explicit instruction in the SOLVE Strategy on the mathematical problem solving skills of six Grade 8 students with specific learning disabilities. The SOLVE Strategy is an explicit instruction, mnemonic‐based learning strategy designed to help students in solving mathematical word problems. Using a multiple probe across participants design, results suggested a functional relation between explicit instruction in the SOLVE strategy and increase in strategy use and computation scores on grade level mathematical word problems for all participants. Additionally, all participants generalized the SOLVE Strategy to other mathematic topics and concepts, and the teacher and students felt the intervention was socially acceptable. Finally, limitations, implications for practice, and suggestions for future research are discussed.  相似文献   

16.
Many have argued that the inclusion of the history of science in science teaching might promote an understanding of the nature of science as well as the attitudes toward science. However, its inclusion in science teaching may not have the desired effect due to the limited coverage it receives in textbooks and the limited time available for teaching. A historical episodes map (HEM) is thus developed with four storylines and more than 20 events related to the history of science and is designed to fit in with regular teaching topics. A total of 329 students in Grade 7 were involved in the experimental group and the control group. The control group was taught using the textbook only, while the experimental group was also taught using the textbook plus HEM materials and associated discussion. The intervention of such teaching lasted for a month and a half. The findings reveal that the exposure of students to HEM materials did promote the students’ understanding of the nature of science as well as their attitudes toward science.  相似文献   

17.
教材选用取向与不同的教材观   总被引：7，自引：0，他引：7  
在实践中,对教师如何选用教材一般存在三种观点:“教教材”、“用教材教”、“不用教材教”。这三种不同观点反映了课程实施过程中三种不同的取向,即“忠实取向”、“调适取向”和“创生取向”。教师对待教材的不同态度实际上也折射了他们不同的教材观。作为新旧两种不同的教材观,“材料式”教材观和“圣经式”教材观在诸多方面都显示出迥然不同的特点。但新的课程改革为教材观的转变提供了政策支持和生存的土壤,“材料式”教材观将成为教师的必然选择。  相似文献   

18.
采用内容分析法和比较法,对湘教版和人教A版普通高中数学选择性必修教科书数学建模内容从内容分布与呈现、情境—问题、建模过程、信息技术使用四个方面进行比较分析。研究发现:两版教科书都以专题形式呈现数学建模内容,问题背景比较复杂、问题类型均为开放式,建模过程注重问题分析和模型建立、关注模型检验,信息技术主要应用在模型建立与求解和模型检验环节。湘教版4个建模专题与三大主线相融合,突出数学建模过程的一般性和案例的示范性,问题情境较为丰富,问题表述形式多样,信息技术软件选择具有开放性;人教A版1个建模专题与统计相联系,突出统计建模案例的示范性和对建模选题做题的指引性,问题情境与科学问题相联系,信息技术软件操作具有示范性。基于此,提出教科书使用建议:一是用好教科书中数学建模专题,发挥示范引领作用;二是组织好课题研究活动,发挥师生能动性。  相似文献   

19.
Electronic textbook usage is increasing within higher education while use of traditional textbooks is declining. While some research concerning student preference for textbook type provides insight into student choices, there is a gap in the literature regarding use of electronic textbooks within dental assisting programs. The purpose of this study was to explore dental assisting students’ preferences regarding electronic textbook usage during their professional education. Two questionnaires were administered to a group of dental assisting students to ascertain their preferences. One questionnaire was given during the Dental Assisting Program orientation at the beginning of the academic year. The second questionnaire was administered at the conclusion of a nine-month dental assisting curriculum in which students were required to use electronic textbooks for approximately half of their courses. Results from the questionnaires indicated that while students were open to the idea of electronic textbooks and willing to use them prior to beginning in the Dental Assisting Program, at the conclusion of the Program they overwhelmingly preferred to use traditional print textbooks.  相似文献   

20.
The authors explore how and to what extent students use their textbooks. Data was collected through a survey regarding when reading is primarily done, how the textbook is used for studying, and which specific study strategies the students used. The results indicate that students know it is important to read, know the professor expects them to read, and know it will impact their grade, yet most students still do not read the textbook. Finally, we also examine what students feel would motivate them to increase their usage of the textbook.  相似文献   

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